Task:

Given the string MI, can you produce the string MU using the following
set of rules ?

Rule 1:If you possess a string whose last letter is I, you can add on
a U at the end

Example: MIII yields MIIIU

Rule 2:Suppose you have Mx, where x represents the entire string
of letters following the M. Then you may add an x to the end of your string.

MIU yields MIUIU

Rule 3:If III occurs in the string, you may replace it with U.

MIII yields MU

or

MIIIU yields MUU

Rule 4:If UU occurs inside the string, you may drop it.

MUUI yields MI

or

MIUU yields MI

A Longer Example:

MI

MII by rule 2

MIIII by rule 2

MUI by rule 3

MUIU by rule 1

MUIUUIU by rule 2

MUIIU by rule 4